Associate Professor
Department of Mathematics
University of Connecticut
West Hartford, CT 06117

From: Perspectives on Science and Christian Faith41.2:99-103
(6/1989)

To say that the universe is "contingent"means
that it need not be the way it

is. A contingent universe does not
contain within itself a sufficient explanationof itself. Although the
doctrine of contingence is an article of faith whichtranscends
scientific demonstration, modern cosmology is making new discoveries
and is asking new questions which point to the contingent character of theuniverse. Does the universe have a "beginning?" Is the extent of
the universe finite? Does mathematical undecidability preclude any
system from containing within itself a sufficient explanation of itself?
Classical physics thought of the universe as closed, necessitarian, and inincontingent.
Thus, certain questions basic to Christian thought were dismissed
out-of-hand as invalid. An incongent universe precludes any revelation from
the outside itself. Modern scientificmodels of the universe offer a
more hospitable arena for the discussion ofChristian theology.

Purpose

I propose to indicate: 1) ways in which modern cosmology points to the
contingence of the universe; and, 2) guidance of the doctrine of contingence can
lend to cosmological thinking.

Definitions

T

To say that the universe is"contingent"
means that it need not be the way it is. Its particular space-time structure is
not a necessary consequence of its existence. Alternately, an
"incontingent" universe would possess a necessary structure; such a
world would be uniquely determined by just the requirement of self-consistency.
A contingent universe does not contain within itself a sufficient explanation of
itself. For an incontingent universe one conceivably could find a single,
consistent theory from which one ' could deduce uniquely the structure of the
world, including the numerical values of all constants of nature. A contingent
universe will here be termed "open;" an incontingent universe will be
termed "closed."

The contingence of the universe has played a
crucial role in the development of modern, experimental science. The majority of
scholars in the ancient world did not appreciate the contingent character of the
world, and so attempted to reason about the world a priori. Modern experimental
science owes a debt to the Medieval doctrine of contingence, as scholars
recognized that to answer questions about nature required asking nature itself.
Although Newton himself denied that "the world exists by necessity and by
the same necessity follows the laws proposed," Newtonians interpreted his
laws as determining the entire structure of the "closed" universe.1
This reductionism was recognized as inadequate only in the wake of
field theory, which appealed to non-particle structures, "fields," as
first suggested by Michael Faraday and later formalized by James Clerk Maxwell.
Today, contingence isan issue between the two options considered by
theoretical cosmologists with regard to the way the universe began. Is there
only one type of universe that is logically possible, which would uniquely
determine all the presently unexplained values of the fundamental constants of
nature? Or are there arbitrary elements in the composition of both the
structure of the universe and its fundamental constants?2

Limitations

If the universe is contingent, and so does not
contain within itself a sufficient explanation of itself, it would seem odd were
we able to prove this fact from within the universe itself. The doctrine of
contingence is an article of faith, which, I believe, transcends scientific
demonstration, and is implied by God's sovereignty in the creatio ex nihilo. Aquinas
held that the very idea that the world did not always exist could be known only
by revelation and not reason.3

Likewise, incontingence begs proof. Those who
favor a "closed" system tend to believe in the "eternity of the
universe," which has been called the "first article of the secular
faith.4 Incontingence has often been a tacit
presupposition of many scientists, but is not inherent to the scientific method.

Our convictions about the contingent nature of
the universe grow out of God's dynamic and free activity rooted in the
revelation of Jesus Christ. Christians believe that the Incarnation was a unique
event which cannot be understood just in terms of this world, as the Arians had
tried to do. The Incarnate Christ transcended this world, and, far from being
explained by it, became the explanation from which the world itself drew its
meaning. The Logos entered into this world, taking upon himself human nature,
and became the Word of God incarnate, speaking to us from within, but above, the
created order.

It is because all contingent realities ...
have their final truth in God's Word rather than in themselves, that in their
employment by the Word himself they may serve the communication to us of a
knowledge of God that is quite beyond us. But because these created realities
which God uses as the medium of his communication have their final truth in
his Word rather than in themselves, they are in themselves far different from
what they · are in our knowledge and formalization of them.5

I do not believe that the contingence of
the universe can be decided by the scientific method. In particular, we should
avoid any attempt to "prove" creatio ex nihilo by an appeal to
"Big Bang"-type theories. At present, cosmology has no adequate
explanation of the origin of the Big Bang. Some cosmologists theorize that in
the Big Bang resulted from quantum relativistic effects in the virtual vacuum.6
Although this model has some experimental support, it remains
controversial among cosmologists. Yet, an appeal to a "God of the
gaps" as the source of the Big Bang (i.e., "The Big Banger"?)
only invites criticism and retraction if a quantum theory of gravity is
successfully formulated.

Cosmological Pointers to Contingence

Although the contingence of the universe is
not decidable scientifically, nevertheless modern cosmology has made new
discoveries and is asking new questions which point to the contingent character
of the universe. These changes in the foundations of cosmology have far-reaching
implications for a unitary understanding of the created universe.

Those who favor a "closed" system
tend to believe in the "eternity of the
universe," which has been called "the
first article of the secular faith."

Through most of the nineteenth century, mechanists thought of
the universe as closed, self-contained, and self-explanatory. Such an eternal
and divine nature bars the possibility of revelation.7
Questions about origin and purpose, which contingence raises, were not even
considered legitimate by the mechanists. Today, however, such questions are
discussed in scientific papers and are regarded as amenable to scientific
inquiry. Questions about first and final causes, which were excluded by a
single-minded emphasis on efficient causes, have returned in discussions about
the Big Bang and the Anthropic Principle.8

The first cosmological indicator of contingence I want to
discuss is time. Mechanists thought of the universe, and hence of time, as
without a beginning. This eternity of space and time is a corollary of
incontingence, as otherwise one is forced to seek an origin of the universe
outside of the universe itself. However, today modern cosmology has found
evidence indicating a finite age of the universe of about 10 to 20 billion
years. This age was arrived at by studying the transformation of the galaxies as
we now observe them. The scientific account "does not go beyond that, to
the singularity when there was nothing and then suddenly the inconceivably
energetic seed for the universe abruptly came into being. Here science seems up
against a blank wall."9

The strongest evidence for the finite age of the universe is
its observed expansion, one of the "great intellectual revolutions" of
this century.10 Mechanists thought of the universe
as static. Einstein's General Theory of
Relativity, published in 1916, predicted an expanding
or contracting universe. But such a conclusion was so unthinkable that Einstein
introduced the 11 cosmological constant," a hypothetical anti-gravityforce, so that a static universe would result11
But in 1922, the Russian physicist Alexander Friedmann mathematically formulated
general relativity without the cosmological constant, and advocated the
expansion of the universe. This idea received observational support in 1929 when
Edwin Hubble analyzed the red shift in the light earth receives from the stars,
and concluded that all galaxies are moving away from earth at a speed directly
proportional to their distance from earth. By extrapolating backwards from this
expansion, one arrives at a singular point of infinite density some IO to 20
billion years ago, the point of origin of the observable universe from which all
matter and energy were thrown out in the "Big Bang." Alternative
theories have been suggested to explain the observed recession of the galaxies.
However, these have failed to account for two further observations, as can the
Big Bang theory: the isotropic background radiation of 2.7' K (for which
discovery Arno Penzias and Robert Wilson of Bell Laboratories were awarded the
Nobel Prize in 1978), and the apparent percentage of hydrogen and helium in the
universe.

Not only do modern cosmologists consider
spacetime as having a beginning, but they recognize a property of time which is
difficult to explain within the universe itself. Physicists speak of
"arrows of time," a term, like "vector," which implies
unidirectionality. In at least two ways the universe induces a direction upon
time which so far appears irreversible. First, by its very origin and subsequent
expansion the universe has an absolute clock" which distinguishes
between prior and subsequent events. 12 Secondly,
the Second Law of Thermodynamics implies that all closed systems proceed
to states of increasing entropy, or disorder. Attempts to explain the
irreversibility of time have not been successful.13Time
irreversibility is an important characteristic for those who see the universe as
an arena for some higher purpose, or teleology, toward which history moves.

.

We should avoid any attempt to prove
creatio ex nihilo by an appeal to "Big Bang"-type theories....
An appeal to a "God of the gaps" as the source
of the Big Bang (i.e., "The Big Banger"?)
only invites criticism and retraction.

A second cosmological indicator of contingence
I want to discuss is the finite extent of the universe. The mechanists of the
last century thought of the universe as being of infinite extent in all
directions. The infinity of space is a corollary of incontingence, as otherwise,
one is forced to consider a "boundary" to the universe and ask about
what lies "beyond" that boundary. General relativity predicts the
universe has finite mass and is finite in extent. Light is no longer thought of
as traveling indefinitely in a straight line, but follows a closed geodesic path
whose curvature is determined by the shape of space-time. If the cosmological
estimates of the Big Bang are correct, and if light speed is the universal
maximum velocity, then the observable universe has a radius of 10 to 20 billion
light years.

A third and final indicator of contingence I
want to discuss is the implication of Godel's tbeorem for cosmology. Toward the
end of the nineteenth century, the "formalist" school of mathematical
interpretation sought to reduce all of mathematics to a single, logical system.
In 1900 David Hilbert posed twenty-three unsolved questions which were to guide
the progress of mathematics into the present day. His second question asked for
a demonstration of the consistency of the axioms of arithmetic. A decade later
Bertrand Russell and Alfred North Whitehead published Principia Mathematica, a
minutely detailed program which showed that all known results of pure
mathematics could be derived from a small number of axioms. But this left
Hilbert's second question unanswered. In 1931 Kurt G6del published the
surprising result that a finite, internal proof of the consistency of the axioms
of arithmetic was impossible. He showed that, in any system large enough to
contain at least the arithmetic axioms, there are statements in the language of
that system whose truth value is undecidable by that system. If then an
undecidable statement is merely appended to that system as an axiom, that
now-larger system will again contain other undecidable propositions. That is,
undecidability cannot be simply "legislated" away.

The far-reaching implications of G6delian
theorems are still being realized. For mathematics, Gbdel's result meant the end
of a purely formalistic interpretation of mathematics as a logical system.
Mathematical truth is larger than any axiomatic system. Stanley Jaki appears as
the first to have developed Godelian implications for cosmology.14There will always be truths about the universe which are beyond any formal
cosmological theory. Seemingly, this supports the contingent character of the
universe, as no single theory could determine completely the structure of the
world. "Doomed also, as a result [of G6del's theorem], is the ideal of
science-to devise a set of axioms from which all phenomena of the natural world
can be deduced."15

There will always be truths about theuniverse which are beyond any formal
cosmological theory.

John Barrow has questioned the relevance of Godel's theorem to
science.16 The type of undecidable proposition
guaranteed by G6def -is self-referencing. Alfred Tarski suggested limiting
admissible statements to only those which do not mix language with
meta-language. Given this restriction, Barrow then asks how we know that there
will be significant undecidable cosmological statements.17He asks rhetorically for just one example of an undecidable proposition
which had stumped mathematicians and had led to a significant scientific
breakthrough. In answer I cite the parallel postulate, the undecidability of
which led to the creation of new geometries which eventually became the language
of relativitv theory. Another significant undecidable proposition is the
Continuum Hypothesis.18

Guidance Contingence Lends Cosmology

The great problem confronting particle physics is the
unification of the four known forces in the universe - electromagnetism,
gravity, weak, and strong interaction-the so-called "unified field
theory." Such would have profound implications for cosmology, as it would
explain the particle interaction during the cosmic cooking" of the cosmic
"yolk" in the Big Bang at which temperatures and density gravitational
attraction between subatomic particles becomes significant. Such a unifying
theory between electromagnetic and weak forces has been experimentally confirmed
("electroweak theory") in recent years at the European Center for
Nuclear Research (CERN). A promising unification between electroweak and strong
forces has been proposed (the " Grand Unification Theory" or GUT).
Accelerators do not have the energy to simulate the temperatures of the cosmic
cooking needed to unify the GUT forces with gravity, which at normal
temperatures are 1039times weaker than electromagnetic force.A unified field theory does not appear to be readily forthcoming,
but nevertheless may be achieved someday.

We must, however, make a distinction between a unified field
theory and a "Theory of Everything," which claims to explain the
structure of the universe uniquely and completely. A Theory of Everything is not
possible in a contingent universe. A belief in such a Theory of Everything
appears "unashamedly in scientific papers, but it is essentially a
religious or metaphysical view, in the sense that it rests only upon an unstated
axiom of faith."19

In 1965 Steve Hawking realized that if he reversed the
direction of time in Roger Penrose's theory about black holes he could describe
the Big Bang singularity. He published a joint paper with Penrose in 1970 which
developed the mathematical techniques to prove that there must have been a Big
Bang singularity provided only that general relativity is correct and the
universe contains only as much matter as we observe.20

It is ironic that the cosmologist who worked
so hard to convince others of the Big Bang singularity has now changed his mind.
For the last ten years, Hawking has speculated about a quantum theory of gravity
which would permit the absorption of a black hole. Furthermore, he surmises that
a time-reversal argument similar to his 1970 paper will account for the
appearance of the Big Bang from quantum gravitational effects in the virtual
vacuum. He seeks, then, to avoid any singularity or beginning to the universe.
In his own words:

The quantum theory of gravity has opened up
a new possibility, in which there would be no boundary to space-time and so
there would be no need to specify the behavior at the boundary. There would be
no singularities at which the laws of science break down and no edge of
space-time at which one would have to appeal to God or some new law to set the
boundary conditions for space-time. The universe would be completely
self-contained and not affected by anything outside itself. It would neither
be created or destroyed. It would just BE.21

Although today it has little experimental
support, such an integration of the quantum and relativity theories would be a
revolutionary intellectual triumph, But Hawking claims too much for it as he
elevates such. integration to a Theory of Everything. In his attempt to get
behind the Big Bang singularity, he thinks he can remove all singularities. I
believe that the doctrine of contingence in a G6delian form would lead us to
expect the scientific enterprise to generate an unending hierarchy of widening
theories, earlier theories being limiting cases of their successors.
Singularities, or point where a theory breaks down, play a vital role in the
pursuit of broader theories. Thus, scientists should seek to get behind
singularities, as they expand their under standing of nature, but should not
expect ultimately tq remove all singularities by achieving some comprehensive
Theory of Everything. We are exploring a universe "open" to an
ever-widening understanding of its infinite pattern and simplicity, not
"closed" within any one self-contained model of its structure.

Conclusion

Modern scientific models of the universe offer
a more hospitable arena for the discussion of Christian theology than did their
predecessors in the last century. When the universe was thought of as closed,
necessitarian, and incontingent certain questions basic to Christian thought
were dismissed out-of-hand as invalid. An incontingent universe precludes any
revelation from outside itself. Today, scientific thinking about the contingent
universe allows a rapprochement with Christian thinking, that together they may
work toward an interdisciplinary understanding of the created universe.

NOTES

1Quoted in
Barrow, John D., The World Within the world, (London:
Oxford University Press, 1988), p. 323.

3 Aquinas, Thomas, Summa Theologica
111, 46, 2. "The reason for this is that the newness of the world
cannot be demonstrated from the world itself. For the principle of demonstration
is the essence of a thing."

8For an
excellent survey, cf. Neidhardt, W. Jim, "The Anthropic Principle: A
Religious Response," Journal of the American Scientific Affiliation, Dec.
1984, pp. 201-207. This paper portrays the contingence of the universe as
intimated by the enormous degree of its specificity, the fascinating details of
which I do not have space here to discuss.

13Barrow, op. cit., p. 367.
Boltzmann has offered a subtle argument in favor of time-reversibility. But this
is a technical question, over which there is little consensus. The interested
reader is referred to the following: Davies, P.C.W., The Physics of Time
Asymmetry, (Berkeley: University of :y California Press, 1974); Brush, Stephen
G., Statistical Physics and the Atomic Theory,
(Princeton: Princeton University Press, 1983); DiFrancia, G. Toraldo, The
Investigation of the Physical World, (Cambridge: Cambridge University
Press, 1976); Prigogine, Ilya and Stengers, Isabelle, Order Out of Chaos, (Toronto:
Bantam Books, 1984).

17At the Consultation on
Theology/Science at the Center of Theological Inquiry, Princeton, Dr. Christoph
Wassermann, of the University of Geneva, pointed out the inherent significance
of self-referencing statements. Whereas a scientific theory may be able to avoid
self-referencing ie statements within itself, as soon as the theory claims to be
true it has made a k self-referencing statement. At the same Consultation, Dr.
David Wilcox, of Eastern College, St. Davids, Pennsylvania, actually used
self-referent statements in his proposed model of the code sequence for amino
acids on the DNA. The definition takes the form of a large riboprotein which can
recognize both the code words and the amino acid which it represents.

18Cohen, P.J., "The
Independence of the Continuum Hypothesis," Proceedings
of the National Academy of Science, 50(1963),
1143-1148; 51(1964), 105-110.